Hasse--Schmidt derivations, divided powers and differential smoothness

Details Hasse--Schmidt derivations, divided powers and differential smoothness Hasse--Schmidt derivations, divided powers and differential smoothness

2009-03-02

arxiv.org/abs/0903.0246v1

Mathematics

Commutative Algebra

Scientific paper

Let $k$ be a commutative ring, $A$ a commutative $k$-algebra and $D$ the filtered ring of $k$-linear differential operators of $A$. We prove that: (1) The graded ring $\gr D$ admits a canonical embedding $\theta$ into the graded dual of the symmetric algebra of the module $\Omega_{A/k}$ of differentials of $A$ over $k$, which has a canonical divided power structure. (2) There is a canonical morphism $\vartheta$ from the divided power algebra of the module of $k$-linear Hasse-Schmidt integrable derivations of $A$ to $\gr D$. (3) Morphisms $\theta$ and $\vartheta$ fit into a canonical commutative diagram.

Affiliated with

Also associated with

No associations

Rating

Hasse--Schmidt derivations, divided powers and differential smoothness does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hasse--Schmidt derivations, divided powers and differential smoothness, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hasse--Schmidt derivations, divided powers and differential smoothness will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-77836